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 Bayesian Inference


Bayesian Optimization Over Iterative Learners with Structured Responses: A Budget-aware Planning Approach

arXiv.org Artificial Intelligence

The rising growth of deep neural networks (DNNs) and datasets in size motivates the need for efficient solutions for simultaneous model selection and training. Many methods for hyperparameter optimization (HPO) of iterative learners, including DNNs, attempt to solve this problem by querying and learning a response surface while searching for the optimum of that surface. However, many of these methods make myopic queries, do not consider prior knowledge about the response structure, and/or perform a biased cost-aware search, all of which exacerbate identifying the best-performing model when a total cost budget is specified. This paper proposes a novel approach referred to as {\bf B}udget-{\bf A}ware {\bf P}lanning for {\bf I}terative Learners (BAPI) to solve HPO problems under a constrained cost budget. BAPI is an efficient non-myopic Bayesian optimization solution that accounts for the budget and leverages the prior knowledge about the objective function and cost function to select better configurations and to take more informed decisions during the evaluation (training). Experiments on diverse HPO benchmarks for iterative learners show that BAPI performs better than state-of-the-art baselines in most cases.


Bayesian Networks for Named Entity Prediction in Programming Community Question Answering

arXiv.org Artificial Intelligence

Within this study, we propose a new approach for natural language processing using Bayesian networks to predict and analyze the context and how this approach can be applied to the Community Question Answering domain. We discuss how Bayesian networks can detect semantic relationships and dependencies between entities, and this is connected to different score-based approaches of structure-learning. We compared the Bayesian networks with different score metrics, such as the BIC, BDeu, K2 and Chow-Liu trees. Our proposed approach out-performs the baseline model at the precision metric. We also discuss the influence of penalty terms on the structure of Bayesian networks and how they can be used to analyze the relationships between entities. In addition, we examine the visualization of directed acyclic graphs to analyze semantic relationships. The article further identifies issues with detecting certain semantic classes that are separated in the structure of directed acyclic graphs. Finally, we evaluate potential improvements for the Bayesian network approach.


Guiding the Sequential Experiments in Autonomous Experimentation Platforms through EI-based Bayesian Optimization and Bayesian Model Averaging

arXiv.org Artificial Intelligence

Autonomous Experimentation Platforms (AEPs) are advanced manufacturing platforms that, under intelligent control, can sequentially search the material design space (MDS) and identify parameters with the desired properties. At the heart of the intelligent control of these AEPs is the policy guiding the sequential experiments, which is to choose the location to carry out the next experiment. In such cases, a balance between exploitation and exploration must be achieved. A Bayesian Optimization (BO) framework with Expected Improvement based (EI-based) acquisition function can effectively search the MDS and guide where to conduct the next experiments so that the underlying relationship can be identified with a smaller number of experiments. The traditional BO framework tries to optimize a black box objective function in a sequential manner by relying on a single model. However, this single-model approach does not account for model uncertainty. Bayesian Model Averaging (BMA) addresses this issue by working with multiple models and thus considering the uncertainty in the models. In this work, we first apply the conventional BO algorithm with the most popular EI-based experiment policy in a real-life fatigue dataset for steel to predict the fatigue strength of steel. Afterward, we apply BMA to the same dataset by working with a set of predictive models and compare the performance of BMA with the traditional BO algorithm, which relies on a single model for approximation. We compare the results in terms of RMSE and find that BMA performs better than EI-based BO in the prediction task by considering the model uncertainty in its framework.


Tailoring Language Generation Models under Total Variation Distance

arXiv.org Artificial Intelligence

The standard paradigm of neural language generation adopts maximum likelihood estimation (MLE) as the optimizing method. From a distributional view, MLE in fact minimizes the Kullback-Leibler divergence (KLD) between the distribution of the real data and that of the model. However, this approach forces the model to distribute non-zero (sometimes large) probability mass to all training samples regardless of their quality. Moreover, in the attempt to cover the low-probability regions in the data distribution, the model systematically overestimates the probability of corrupted text sequences, which we conjecture is one of the main reasons for text degeneration during autoregressive decoding. To remedy this problem, we leverage the total variation distance (TVD) with its robustness to outliers, and develop practical bounds to apply it to language generation. Then, we introduce the TaiLr objective that balances the tradeoff of estimating TVD. Intuitively, TaiLr downweights real data samples that have low model probabilities with tunable penalization intensity. Experimental results show that our method alleviates the overestimation of degenerated sequences without sacrificing diversity and improves generation quality on a wide range of text generation tasks.


Q-Cogni: An Integrated Causal Reinforcement Learning Framework

arXiv.org Artificial Intelligence

We present Q-Cogni, an algorithmically integrated causal reinforcement learning framework that redesigns Q-Learning with an autonomous causal structure discovery method to improve the learning process with causal inference. Q-Cogni achieves optimal learning with a pre-learned structural causal model of the environment that can be queried during the learning process to infer cause-and-effect relationships embedded in a state-action space. We leverage on the sample efficient techniques of reinforcement learning, enable reasoning about a broader set of policies and bring higher degrees of interpretability to decisions made by the reinforcement learning agent. We apply Q-Cogni on the Vehicle Routing Problem (VRP) and compare against state-of-the-art reinforcement learning algorithms. We report results that demonstrate better policies, improved learning efficiency and superior interpretability of the agent's decision making. We also compare this approach with traditional shortest-path search algorithms and demonstrate the benefits of our causal reinforcement learning framework to high dimensional problems. Finally, we apply Q-Cogni to derive optimal routing decisions for taxis in New York City using the Taxi & Limousine Commission trip record data and compare with shortest-path search, reporting results that show 85% of the cases with an equal or better policy derived from Q-Cogni in a real-world domain.


Mitigating Observation Biases in Crowdsourced Label Aggregation

arXiv.org Artificial Intelligence

Crowdsourcing has been widely used to efficiently obtain labeled datasets for supervised learning from large numbers of human resources at low cost. However, one of the technical challenges in obtaining high-quality results from crowdsourcing is dealing with the variability and bias caused by the fact that it is humans execute the work, and various studies have addressed this issue to improve the quality by integrating redundantly collected responses. In this study, we focus on the observation bias in crowdsourcing. Variations in the frequency of worker responses and the complexity of tasks occur, which may affect the aggregation results when they are correlated with the quality of the responses. We also propose statistical aggregation methods for crowdsourcing responses that are combined with an observational data bias removal method used in causal inference. Through experiments using both synthetic and real datasets with/without artificially injected spam and colluding workers, we verify that the proposed method improves the aggregation accuracy in the presence of strong observation biases and robustness to both spam and colluding workers.


Transport Reversible Jump Proposals

arXiv.org Machine Learning

Reversible jump Markov chain Monte Carlo (RJMCMC) proposals that achieve reasonable acceptance rates and mixing are notoriously difficult to design in most applications. Inspired by recent advances in deep neural network-based normalizing flows and density estimation, we demonstrate an approach to enhance the efficiency of RJMCMC sampling by performing transdimensional jumps involving reference distributions. In contrast to other RJMCMC proposals, the proposed method is the first to apply a non-linear transport-based approach to construct efficient proposals between models with complicated dependency structures. It is shown that, in the setting where exact transports are used, our RJMCMC proposals have the desirable property that the acceptance probability depends only on the model probabilities. Numerical experiments demonstrate the efficacy of the approach.


Noise-Aware Statistical Inference with Differentially Private Synthetic Data

arXiv.org Artificial Intelligence

While generation of synthetic data under differential privacy (DP) has received a lot of attention in the data privacy community, analysis of synthetic data has received much less. Existing work has shown that simply analysing DP synthetic data as if it were real does not produce valid inferences of population-level quantities. For example, confidence intervals become too narrow, which we demonstrate with a simple experiment. We tackle this problem by combining synthetic data analysis techniques from the field of multiple imputation (MI), and synthetic data generation using noise-aware (NA) Bayesian modeling into a pipeline NA+MI that allows computing accurate uncertainty estimates for population-level quantities from DP synthetic data. To implement NA+MI for discrete data generation using the values of marginal queries, we develop a novel noise-aware synthetic data generation algorithm NAPSU-MQ using the principle of maximum entropy. Our experiments demonstrate that the pipeline is able to produce accurate confidence intervals from DP synthetic data. The intervals become wider with tighter privacy to accurately capture the additional uncertainty stemming from DP noise.


DS-K3DOM: 3-D Dynamic Occupancy Mapping with Kernel Inference and Dempster-Shafer Evidential Theory

arXiv.org Artificial Intelligence

Occupancy mapping has been widely utilized to represent the surroundings for autonomous robots to perform tasks such as navigation and manipulation. While occupancy mapping in 2-D environments has been well-studied, there have been few approaches suitable for 3-D dynamic occupancy mapping which is essential for aerial robots. This paper presents a novel 3-D dynamic occupancy mapping algorithm called DS-K3DOM. We first establish a Bayesian method to sequentially update occupancy maps for a stream of measurements based on the random finite set theory. Then, we approximate it with particles in the Dempster-Shafer domain to enable real-time computation. Moreover, the algorithm applies kernel-based inference with Dirichlet basic belief assignment to enable dense mapping from sparse measurements. The efficacy of the proposed algorithm is demonstrated through simulations and real experiments.


Robustness to corruption in pre-trained Bayesian neural networks

arXiv.org Artificial Intelligence

ShiftMatch is inspired by the training-data-dependent "EmpCov" priors from Izmailov et al. (2021a), and efficiently matches test-time spatial correlations to those at training time. Critically, ShiftMatch is designed to leave the neural network's training time likelihood unchanged, allowing it to use publicly available samples from pre-trained BNNs. Using pre-trained HMC samples, ShiftMatch gives strong performance improvements on CIFAR-10-C, outperforms EmpCov priors (though ShiftMatch uses extra information from a minibatch of corrupted test points), and is perhaps the first Bayesian method capable of convincingly outperforming plain deep ensembles. Neural networks are increasingly being deployed in real-world, safety-critical settings such as selfdriving cars (Bojarski et al., 2016) and medical imaging (Esteva et al., 2017). BNNs are indeed highly effective at improving uncertainty estimation in the in-distribution setting, where the train and test distributions are equal (Zhang et al., 2019; Izmailov et al., 2021b). Critically, we also need to continue to perform effectively (or at least degrade gracefully) when presented with corrupted inputs. Superficially, BNNs seem like a good choice for this setting: we would hope they would give more uncertainty in regions far from the training data, and thus degrade gracefully as inputs become gradually more corrupted, and thus diverge from the training data. However, recent work has highlighted that BNNs including with gold-standard Hamiltonian Monte Carlo (HMC) inference can fail to generalise to corrupted images, potentially performing worse than ensembles (Lakshminarayanan et al., 2017; Ovadia et al., 2019; Izmailov et al., 2021a;b). Izmailov et al. (2021a) gave a key intuition as to why this failure might occur. In particular, consider directions in input space with zero variance under the training data.